Robust localized adaptive waveform inversion: A new regularization for Gabor deconvolution

Recently, we have developed a localized adaptive waveform inversion method (LAWI) to tackle the cycle-skipping issue in velocity reconstruction by waveform inversion. In LAWI, the Gabor deconvolution is applied to compute a local matching filter, whose centroid time is used for measuring the instantaneous time shift between observed and calculated data. Different from AWI which is based on a stationary convolutional model, LAWI can take the non-stationarity nature of seismic data into account, therefore performing better in handling realistic cycle skipping problems. Numerical tests show that, compared with AWI, the application of LAWI seems to require a higher signal-to- noise ratio (SNR) of observed data. To make LAWI work for low-SNR data, a delta-type regularization is developed to deal with the noise problems inherent in the Gabor deconvolution. Despite a slight resolution loss and a “layer-stripping principle break” induced by this new regularization illustrated numerically, we present how this method can be useful to invert low-SNR data on the Chevron benchmark dataset.